A regular critic of Reasons To Believe recently sent a comment to the last post that I would like to quote here because of its significance and its focus. The critique centers on RTB's use (or alleged misuse) of probability theory. The skeptic goes on to say that events with zero probability indeed happen every day.
Although this space is ostensibly a place where Average Joes can hang out, it's perfectly fine to explore an issue in depth even if it leaves people like me scratching their heads. Here's part of Bob's argument:
RTB’s position certainly is “The probability of our existence occurring by chance is nearly zero. We see fine-tuning everywhere. These facts strongly imply God exists.” Here are a few quotes from Hugh Ross himself:
As to Hugh’s probability estimates . . . Just because he is trained in astronomy doesn’t mean he knows all things math, including probability. That is fallacious reasoning. Most physicists I know don’t understand probability theory.
Roger writes: “As to probabilities: essentially all scientists agree that, if an event has less than one chance in 10 to the 50th of happening, we can’t realistically expect that the event has ever occurred or will ever occur—unless totally unexpected or undetected factors are present or introduced.”
Essentially all scientists are wrong then. Here is one better. How about an event that has zero probability? It is clear from your comments that you would never expect an event with zero probability to ever occur—and I expect the same belief for every follower of RTB. But, hear ye hear ye, events with zero probability occur every single day, and these aren’t theoretical or pathological events. Did you know this? Does anyone at RTB know this? How can this be? If an event with zero probability can occur every single day, then can’t an event with non-zero probability occur every single day too? That really throws a monkey wrench into the probability-argument machine of RTB. Anyone who has taken an undergraduate class in probability theory can explain why, and point out the serious flaws in Hugh Ross’s multiplication of meaningless numbers.
Let’s go further with a simple example of hypothesis testing. RTB argues, while wearing the latest emperor’s fashions, for the hypothesis that the Christian God exists. Call this hypothesis H. RTB bases its argument for H on the evidence that we are here. Call this X. Using a fundamental and powerful law of probability called Bayes’ Theorem—who was actually a Presbyterian preacher— we can say the following:
- P(H | X) P(X) = P(X | H) P(H).
In words this means: the product of the probability that God exists given that we exist and the probability that we exist is equal to the product of the probability that we exist given God exists and the probability that God exists. RTB wants to show that P(H | X) is very high, and thus believable. In other words, that our very existence proves that the Christian God exists. So that means we have the following relation to compute:
- P(H | X) = P(X | H) P(H) / P(X).
Which of the numbers on the right-hand side can we actually quantify? We can all agree that the probability we exist given God exists is one: P(X | H) = 1. This leaves us with this expression:
- P(H | X) = P(H) / P(X).
Now, what is the probability that God exists P(H)? And what is the probability that we exist P(X)? Numbers cannot be assigned to these terms. RTB tries to calculate P(X), but in absolutely nonsensical ways . Making matters worse, since probability is a value between 0 and 1, P(H) must be less than or equal to the probability of our existence P(X). In other words, the probability of the existence of God must be less than the probability of our existence (with the assumption that P(X | H) = 1). This is a huge problem for RTB! Even bigger than the first one discussed above.
Does no one here or at RTB possess even a fundamental understanding of probability theory. Probability theory is the single most important scientific and mathematical advancement of the 20th century! Probability theory is the reason why computers and computer networks, cellular telephony, modern medicine, and many many more things actually work. It has paved the way for revolutions in science (quantum mechanics, statistical mechanics, genetics), technology (digital electronics, the Internet), and economics (market theory, mutual funds, insurance), and many other areas. If the pharmaceutical industry did not properly apply the concepts of probability theory the consequences would be dire — lives would be devastated. I would think an organization that proclaims the value of scientific truth would understand the importance of properly and honestly applying probability theory.
OK, readers. There it is. Any responses?